Perfectly safe. I know tons of women who go travelling by themselves. I don't know Paris so can't help there. When it comes to meeting people you might encounter some problems. If I was in a similar situation I'd consider staying in a hostel. Great way to meet people and pretty cheap but you have a booked hotel room and you might want the luxury of a hotel room. Lonely planet are normally a good go to. You could also get an app called triposo.
Get a city map and walk. That's normally quite a good thing to do. You might want to plan your trip a little so you can see everything.